A pentagon has actually 5 sides, and can be made indigenous three triangles, therefore you know what ...

You are watching: If the sum of the interior angles of a polygon is 540 then how many sides does the polygon have

... Its interior angles add up to 3 × 180° = 540°

And as soon as it is regular (all angles the same), climate each edge is 540° / 5 = 108°

(Exercise: make certain each triangle below adds up to 180°, and also check the the pentagon"s internal angles include up to 540°)

The inner Angles the a Pentagon include up come 540°

## The basic Rule

Each time we include a next (triangle come quadrilateral, square to pentagon, etc), we add another 180° to the total:

ShapeSidesSum ofInterior AnglesShapeEach Angle
 If that is a Regular Polygon (all sides room equal, all angles room equal) Triangle 3 180° 60° Quadrilateral 4 360° 90° Pentagon 5 540° 108° Hexagon 6 720° 120° Heptagon (or Septagon) 7 900° 128.57...° Octagon 8 1080° 135° Nonagon 9 1260° 140° ... ... .. ...See more: Dog Attack Dream Of Being Attacked By A Dog Attacking You? What Does It Mean To Dream That A Dog Attacks You ... Any Polygon n (n−2) × 180° (n−2) × 180° / n

So the general dominance is:

Sum of internal Angles = (n−2) × 180°

Each angle (of a continuous Polygon) = (n−2) × 180° / n

Perhaps an example will help:

### Example: What about a constant Decagon (10 sides) ? Sum of inner Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
= 1440°

And because that a regular Decagon:

Each interior angle = 1440°/10 = 144°

Note: inner Angles space sometimes called "Internal Angles"

interior Angles Exterior Angles levels (Angle) 2D forms Triangles square Geometry Index